The Computation of Quantum Chemistry for The Intersystem Crossing Transition

In this paper, it is reported that the theoretical research on the electronic transitions between the different multiple states has been handled by means of perturbational method in the quantum chemistry. Considering the coupling between a mono-excited singlet state and a mono- excited triplet state, the wave functions of the perturbed singlet and triplet state are shown by the following respectively:\beginaligned & ^1 U_I= ^1 \psi_I+\sum_M \sum_T r \frac\left( ^3 \psi_M^T r\left|\hatH^\prime\right|^1 \psi_I\right) ^1 E_I- ^3 E_M ^3 \psi_M^T r \\ & ^3 U_I^T r= ^3 \psi_I^T r+\sum_K \frac\left( ^1 \psi_K\left|\hatH^\prime\right|^3 \psi_I^T r\right) ^3 E_I- ^1 E_K ^1 \psi_K\endalignedwhere¹ψ_I and³ψ_I^Trr represent the wave function of the singlet state and Tr-th compont of the wave function of the triplet state respetively; Tr=+1, 0, -1; E_I is the energy of the I-th state; the summations run over all considered states; the \hatH' is the coupling operator between the orbital and the spin and it is represented by \hatH^\prime=\sum_P \xi_P\left(r_P\right) \vecL_P \cdot \vecS_P where \xi_p\left(r_p\right)=\frac12 m^2 c^2 \frac1r_p \fracd ud r_p and L_p and S_p represent the operators of the angular momentum of the orbital and spin, respresently.
The coupling transition moment between a mono-excitcd singlet state and corresponding triplet exited state is \beginaligned ^Tr \mathbfM_I\left( ^1 u_I ^3 u_I^T_r\right)= & \sum_k=1^N \frac\left( ^1 \psi_k\left|\hatH^\prime\right|^3 \psi_I^T_r\right)^\cdot ^3 E_I- ^1 E_k \mathbfM_I\left( ^1 \psi_k, ^1 \psi_I\right) \\ & +\sum_k=1^N \frac\left( ^3 \psi_k^T_r\left|\hatH^\prime\right|^1 \psi_I\right) ^1 E_I- ^3 E_k \mathbfM_I\left( ^3 \psi_I^T_r, ^3 \psi_k^T_r\right)\endaligned where i (=x, y, z) is the directional index and T is the index of triplet state component as mentioned above; N is the number of the configurations involved in configuration interaction.
We expand the wave functions in the coupling representaion with those in the non-coueling representation for the first time, and compute the elements of the perturbing matrics. It is possible by the methods mentioned above to compute the S_i→T_i transition process which is difficultly researched by means of experimental methods, and the good results can be obtained.